Problem: Nauuo is a girl who loves playing chess.

One day she invented a game by herself which needs n chess pieces to play on a m× m chessboard. The rows and columns are numbered from 1 to m. We denote a cell on the intersection of the r-th row and c-th column as (r,c).

The game's goal is to place n chess pieces numbered from 1 to n on the chessboard, the i-th piece lies on (r_i,\,c_i), while the following rule is satisfied: for all pairs of pieces i and j, |r_i-r_j|+|c_i-c_j|≥|i-j|. Here |x| means the absolute value of x.

However, Nauuo discovered that sometimes she couldn't find a solution because the chessboard was too small.

She wants to find the smallest chessboard on which she can put n pieces according to the rules.

She also wonders how to place the pieces on such a chessboard. Can you help her?

Input

The only line contains a single integer n (1≤ n≤ 1000) — the number of chess pieces for the game.

Output

The first line contains a single integer — the minimum value of m, where m is the length of sides of the suitable chessboard.

The i-th of the next n lines contains two integers r_i and c_i (1≤ r_i,c_i≤ m) — the coordinates of the i-th chess piece.

If there are multiple answers, print any.

Examples

Input


2


Output


2
1 1
1 2

Input


4


Output


3
1 1
1 3
3 1
3 3

Note

In the first example, you can't place the two pieces on a 1×1 chessboard without breaking the rule. But you can place two pieces on a 2×2 chessboard like this:

<image>

In the second example, you can't place four pieces on a 2×2 chessboard without breaking the rule. For example, if you place the pieces like this:

<image>

then |r_1-r_3|+|c_1-c_3|=|1-2|+|1-1|=1, |1-3|=2, 1<2; and |r_1-r_4|+|c_1-c_4|=|1-2|+|1-2|=2, |1-4|=3, 2<3. It doesn't satisfy the rule.

However, on a 3×3 chessboard, you can place four pieces like this:

<image>

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.*;
public class B564{
	
	static class FastReader{
		BufferedReader br;
		StringTokenizer st;
		public FastReader(){
			br=new BufferedReader(new InputStreamReader(System.in));
		}
		String next(){
			while(st==null || !st.hasMoreElements()){
				try{
					st= new StringTokenizer(br.readLine());
				}
				catch (IOException e){
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}
		int nextInt(){
			return Integer.parseInt(next());
		}
		long nextLong(){
			return Long.parseLong(next());
		}
		double nextDouble(){
			return Double.parseDouble(next());
		}
		String nextLine(){
			String str = "";
			try{
				str=br.readLine();
			}
			catch(IOException e){
				e.printStackTrace();
			}
			return str;
		}
	}

	static class pair{
		int first,second;
		pair(int f,int s){
			first=f;
			second=s;
		}
	}

	public static long fastexpo(long x, long y, long p){
		long res=1;
		while(y > 0){
			if((y & 1)==1)
				res= ((res%p)*(x%p))%p;
			y= y >> 1;			
			x = ((x%p)*(x%p))%p;
		}
		return res;
	}

	public static boolean[] sieve (int n) {
		boolean primes[]=new boolean[n+1];
		Arrays.fill(primes,true);
		primes[0]=primes[1]=false;
		for(int i=2;i*i<=n;i++){
			if(primes[i]){
				for(int j=i*i;j<=n;j+=i)
					primes[j]=false;
			}
		}
		return primes;
	}

	public static long gcd(long a,long b){
        return (BigInteger.valueOf(a).gcd(BigInteger.valueOf(b))).longValue();
    }

    public static void merge(int a[],int l,int m,int r){
        int n1,n2,i,j,k;
        n1=m-l+1;
        n2=r-m;

        int L[]=new int[n1];
        int R[]=new int[n2];

        for(i=0;i<n1;i++)
            L[i]=a[l+i];
        for(j=0;j<n2;j++)
            R[j]=a[m+1+j];

        i=0;j=0;

        k=l;
        while(i<n1&&j<n2){
            if(L[i]<=R[j]){
                a[k]=L[i];
                i++;
            }
            else{
                a[k]=R[j];
                j++;
            }
            k++;
        }

        while(i<n1){
            a[k]=L[i];
            i++;
            k++;
        }
        while(j<n2){
            a[k]=R[j];
            j++;
            k++;
        }
    }
    public static void sort(int a[],int l,int r){
        int m;
        if(l<r){
            m=(l+r)/2;
            sort(a,l,m);
            sort(a,m+1,r);

            merge(a,l,m,r);
        }
    }

    
	
	public static void main(String args[]){
		FastReader sc = new FastReader();
		int n,gr,i,count;
		n=sc.nextInt();
		gr=1+n/2;
		System.out.println(gr);
		count=0;
		for(i=1;i<=gr&&count<n;i++){
			System.out.println(1+" "+i);
			count++;
		}
		for(i=2;i<=gr&&count<n;i++){
			System.out.println(i+" "+gr);
			count++;
		}
	}
}